We study the magnetic excitations on top of the plateaux states recently discovered in spin-Peierls systems in a magnetic field. We show by means of extensive density matrix renormalization group (DMRG) computations and an analytic approach that one single spin-flip on top of $M=1-frac2N$ ($N=3,4,...$) plateau decays into $N$ elementary excitations each carrying a fraction $frac1N$ of the spin. This fractionalization goes beyond the well-known decay of one magnon into two spinons taking place on top of the M=0 plateau. Concentrating on the $frac13$ plateau (N=3) we unravel the microscopic structure of the domain walls which carry fractional spin-$frac13$, both from theory and numerics. These excitations are shown to be noninteracting and should be observable in x-ray and nuclear magnetic resonance experiments.
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